Question

1. calculate the vertical asymptote(s) of the rational function $f(x)=\frac{x^2 - 1}{x^2 - 6x - 7}$.$\bigcirc$ $x=-1, x=1LXB0\bigcirc$ $x=7$$\bigcirc$ $x=1$

Explanation:

Step1: Factor numerator and denominator

Numerator: $x^2-1=(x-1)(x+1)$
Denominator: $x^2-6x-7=(x+1)(x-7)$

Step2: Simplify the function

$f(x)=\frac{(x-1)(x+1)}{(x+1)(x-7)}=\frac{x-1}{x-7}$, $x
eq-1$

Step3: Find vertical asymptote

Set simplified denominator to 0: $x-7=0$
Solve for $x$: $x=7$

Answer:

$x=7$